A046268 Largest prime substring in 2^n (or 0 if none exist).

0, 2, 0, 0, 0, 3, 0, 2, 5, 5, 2, 2, 409, 19, 163, 7, 6553, 131, 2621, 5, 857, 971, 419, 83, 1677721, 5443, 71, 1342177, 43, 709, 107, 83, 4294967, 89, 171798691, 3597383, 6871947673, 3743895347, 779069, 54975581, 511627, 99023, 4398046511, 79609, 18604441, 883

Offset

0,2

Links

Michael S. Branicky, Table of n, a(n) for n = 0..2000

Formula

a(n) = A047814(2^n). - Pontus von Brömssen, Jan 16 2025

Example

2^37 = 1{3743895347}2, so a(37) = 3743895347.

Prog

(Python)
from sympy import isprime
def a(n):
    s = str(2**n)
    ss = (int(s[i:j]) for i in range(len(s)) for j in range(i+1, len(s)+1))
    return max((k for k in ss if isprime(k)), default=0)
print([a(n) for n in range(46)]) # Michael S. Branicky, Sep 20 2022

Crossrefs

Cf. A000079, A046260, A047814.

Sequence in context: A348341 A330936 A284687 * A202425 A292374 A292376

Adjacent sequences: A046265 A046266 A046267 * A046269 A046270 A046271

Keyword

nonn,changed

Author

Patrick De Geest, Jun 15 1998

Extensions

a(44) and beyond from Michael S. Branicky, Sep 20 2022

Status

approved